Functional Constraints Research Articles

The velocity tracking problem for Navier–Stokes equations with pointwise-integral control constraints in time-space

In this work, we study the velocity tracking control problem of the evolutionary two-dimensional Navier–Stokes system. The regularizing Tikhonov term is not involved in the cost functional and pointwise-integral control constraints in time-space are considered. First- and second-order optimality conditions are established using a suitable extended cone for the sufficient ones. We also address the numerical approximation of the control problem, proving the convergence of the discrete problems and establishing error estimates between the optimal discrete and continuous states.

Vehicle Trajectory Prediction Using Residual Diffusion Model Based on Image Information

In automatic driving, accurate prediction of vehicle trajectory is the key to achieve automatic driving, and multi-vehicle joint trajectory prediction has become an important part of modern human-computer interaction systems such as automatic driving. In order to better predict vehicle trajectories, we propose a new residual diffusion model to infer the joint distribution of future multi-vehicle trajectories. This approach has several major advantages. First, the model is able to learn multiple probability distributions from trajectory data to obtain potential outcomes for vehicles to multiple future trajectories. Secondly, in order to integrate the motion characteristics of multiple vehicles in the same scene, we use the method of combining the reference denoising and multiple residual denoising to improve the model performance and prediction speed. Finally, on this basis, a general trajectory constraint function is introduced, so that the generated trajectories of multiple vehicles will not collide with each other. We perform a rich experimental comparison of various existing methods on the NGSIM dataset and demonstrate that the proposed algorithm achieves a 26% improvement on mAP.

Functional Outcome of Cast Immobilisation and Functional Treatment in Management of Lateral Ankle Sprain (Grade 1 and 2)

Background: Pain and functional constraints from ankle sprains, which mostly impact the lateral ligamentous complex, can lead to the consumption of medical facilities and unavailability from workplace. No single technique is regarded as the most effective, despite the fact that this injury occurs frequently. This study evaluates the management modalities for lateral ankle sprain i.e. functional treatment and cast immobilization with pain and function as outcome variables.  Materials and methods: Seventy patients with lateral ankle sprains (grade 1 and 2) were included in this study. Each alternate participant was placed in a functional treatment (group A), while the other participants were placed in a cast immobilization group (group B). Every patient was assessed at a follow up of 2 and 6 weeks using Visual analog scale and Karlsson score for quantifying pain and function respectively.  Results: Thirty-two patients in the functional therapy group and twenty-eight in the cast immobilization group finished the study. The functional therapy group's mean age was 27.7 years, while the cast immobilization group's was 29.4 years. While both the right and left ankles were similarly impacted in the cast immobilization group, the dominant ankle involved in the functional treatment group was the right ankle in 19 patients and the left ankle in 16 patients. In both groups, a male preponderance was seen. By the end of the study, the mean differences between the two groups' Karlsson scores and visual analog scale scores were statistically significant.  Conclusion: Our study's findings show that a functional treatment outperforms immobilization in terms of both functional outcome and pain reduction.

Skill matters: Dynamic skill learning for multi-agent cooperative reinforcement learning

With the popularization of intelligence, the necessity of cooperation between intelligent machines makes the research of collaborative multi-agent reinforcement learning (MARL) more extensive. Existing approaches typically address this challenge through task decomposition of the environment or role classification of agents. However, these studies may rely on the sharing of parameters between agents, resulting in the homogeneity of agent behavior, which is not effective for complex tasks. Or training that relies on external rewards is difficult to adapt to scenarios with sparse rewards. Based on the above challenges, in this paper we propose a novel dynamic skill learning (DSL) framework for agents to learn more diverse abilities motivated by internal rewards. Specifically, the DSL has two components: (i) Dynamic skill discovery, which encourages the production of meaningful skills by exploring the environment in an unsupervised manner, using the inner product between a skill vector and a trajectory representation to generate intrinsic rewards. Meanwhile, the Lipschitz constraint of the state representation function is used to ensure the proper trajectory of the learned skills. (ii) Dynamic skill assignment, which utilizes a policy controller to assign skills to each agent based on its different trajectory latent variables. In addition, in order to avoid training instability caused by frequent changes in skill selection, we introduce a regularization term to limit skill switching between adjacent time steps. We thoroughly tested the DSL approach on two challenging benchmarks, StarCraft II and Google Research Football. Experimental results show that compared with strong benchmarks such as QMIX and RODE, DSL effectively improves performance and is more adaptable to difficult collaborative scenarios.

Robust proximity rendezvous and coordinated control of space robots

This paper investigates the robust proximity rendezvous and coordinated control of space robots. A robust rendezvous controller is meticulously devised to guarantee the H∞ performance of space rendezvous mission by addressing the Hamilton–Jacobi–Isaacs inequality. Additionally, a virtual control system is formulated to guarantee that the robust control inputs adhere to saturation constraints. Furthermore, this study introduces a novel fixed-time convergence constraint function aimed at constraining coordinated tracking missions for end-effector. The proposed coordinated controller ensures the achievement of end-effector pose tracking within a predetermined fixed time, while concurrently stabilizing the base attitude and bounding the transient responses of tracking errors within user-defined ranges. Notably, all these accomplishments are demonstrated under conditions of parameter uncertainty and input disturbance. Simulation results validate the effectiveness of the proposed control scheme.

Automated Layout Design of Hydraulic Components With Constraints on Flow Channels

Abstract The lightweight design of hydraulic equipment has always been of vital interest. Additive manufacturing (AM) technology can meet the manufacturing requirements of heteroideus and lightweight hydraulic equipment. However, traditional layout optimization often cannot satisfy the functional constraints of hydraulic components. This article proposes a design method of function-based automatic layout optimization for hydraulic components to solve this problem. The proposed method combines multi-component layout optimization with flow-up channel path planning and uses the triangular mesh model of hydraulic components directly as layout units. The spatial pose of the layout unit is used as the gene sequence for a genetic algorithm (GA). To meet the functional constraints, this study also proposes a fast, accurate collision detection algorithm for irregular 3D models and the generating strategy for follow-up flow channels. Here, the volume of the layout units, the total centroid radius of the layout plan, the length of flow channels, and the pressure loss are taken as the objective functions, and an automatic layout optimization algorithm for hydraulic components is developed. By optimizing the initial layout plan of an aviation electro-hydrostatic actuator (EHA), the characteristic volume of the optimized layout is reduced by 30.68% and the total length of the flow channels is decreased by 39.53%, demonstrating the efficiency of this method for lightweight hydraulic equipment design.

3-D full-field reconstruction of chemically reacting flow towards high-dimension conditions through machine learning

Monitoring chemically reacting flow is crucial for optimizing and controlling the conversion processes in various chemical engineering scenarios. These processes are often influenced by multiple factors, creating a high-dimensional condition space that imposes intensive computational cost to computational fluid dynamics (CFD) methods. We present a machine learning (ML) framework to reconstruct the 3-D scalar field preserving the accuracy and resolution of CFD modeling. We demonstrate the framework’s effectiveness through a case study on biomass combustion in an industrial-scale grate furnace, which exemplifies the challenges of modeling chemically reacting flow in complex geometric domains influenced non-linearly by multiple parameters. The framework implements three core principles: (1) a Reactor-Structure-Resembled Network (RSRNet) reflecting the operational logics of the reactor, (2) an incremental learning strategy based on random Latin Hypercube Sampling, and (3) the incorporation of self-extracted high-level features from data as soft constraints in the loss function. Ground truth data were calculated through a CFD model, with all cases sampled from a 11-variable condition space. Using only 240 randomly sampled cases (around 1 % total cases in the discretized condition space), RSRNet precisely replicated 1-D and 2-D scalar distributions through incremental training. Further reconstruction of 3-D temperature field only used 40 3-D CFD cases, resulting in the training and testing errors decreased to 7.94 × 10-4 and 1.55 × 10-3, respectively, approaching the level of the 2-D reconstruction, with the average error in temperature field predictions not exceeding 50 K. The generalization ability was validated using a separate test dataset with continuously changing excess air ratio and capacity ratio in wide ranges, including some extreme values, and the model successfully captured complex phenomena under unseen conditions.

Adaptive Free-Form Deformation Parameterization Based on Spring Analogy Method for Aerodynamic Shape Optimization

An adaptive Free-Form Deformation parameterization method based on a spring analogy is presented for aerodynamic shape optimization problems. The proposed method effectively incorporates the gradients of the objective and constraint functions, achieving automatic control point adjustment based on variances in design variable components. To evaluate the performance of the adaptive FFD parameterization method, two 2D airfoil optimization design problems are examined. The optimization of the RAE2822 airfoil with 12, 18 and 24 design variables demonstrates superior results for the adaptive method compared to uniform parameterization. The adaptive method requires fewer iterations and achieves lower objective function values. Additionally, the optimization design from NACA0012 to RAE2822 airfoil with 18 design variables shows that the adaptive parameterization method achieves a lower drag coefficient while satisfying the optimization objective. This validates the method’s capability to finely adjust airfoil shapes and capture more optimal design points by exerting stronger control over local shapes. The proposed adaptive FFD parameterization method proves highly effective for optimizing aerodynamic shapes, offering stability and efficiency in the early stages of optimization, even with a limited number of design variables.

Integrated automatic parking path planning and trajectory tracking optimization method

Current automatic parking systems often separate path planning and trajectory tracking, increasing complexity and failing to meet the parking needs of autonomous cars. Consequently, this study presents an approach based on Multi-stage Nonlinear Model Predictive Control (MSNMPC) for integrated autonomous parking path planning and trajectory tracking optimization. The method represents the evolution of uncertainty parameters over time through a scenario tree, and the MSNMPC controller with a predictive horizon P defines P + 1 phases, each with specific cost and constraint functions that depend only on the vehicle state and control inputs of that phase to satisfy the constraints of all phases of the parking process. In addition, the method integrates path planning and tracking control into one optimization problem, which is solved online to achieve integrated parking control. Simulation confirms that, in comparison to MPC with RRT* hierarchical control, the integrated parking scheme of MSNMPC has less lateral error and offers superior flexibility and tracking performance. To verify the generality of the scheme, it was validated in the diagonal parking scenario and the vertical parking scenario, respectively. The results show that, compared to the control experiments, the parking elapsed time has been reduced by 10.76% and 9.02%, respectively, enhancing parking efficiency. In addition, the parking error has decreased by 30.77% and 38.46%, respectively, thus improving parking accuracy. Moreover, the minimum safe distance in the control scheme for addressing uncertainty factors is 0.7 m greater than that of the control experiments, meeting the driving requirements for driverless vehicles in parking scenarios.

Awake surgery with mapping-based resection to treat focal epilepsy in eloquent brain areas.

Resective surgery is a potential therapeutic option for select patients with intractable focal epilepsy. However, the presence of ictal onset zones within or surrounding highly functional brain areas presents a surgical challenge, leading to poor seizure and functional outcomes. This report describes our experiences with awake mapping-tailored resection of epileptogenic areas involving eloquent cortices and evaluates their feasibility, tolerance, limitations, and significance. The study included patients who underwent surgery for drug-resistant focal epilepsy at our center under awake conditions. The surgical approach aimed to achieve maximum resection of preoperatively defined epileptogenic zones, considering the boundaries defined by surrounding functional areas. We collected data on preoperative evaluations, intraoperative tests and seizures, postoperative status epilepticus, and neurological functional outcomes. We included 22 patients, 10 of whom had non-lesional epilepsy. Language, motor function, and sensory function were at risk in 19, 9, and 4 patients, respectively. Resection was performed as planned in 14 (63.6%) patients, while modifications were necessary in 8 (36.4%) patients due to functional constraints. The mean follow-up duration was 29.8months. Sixteen (72.7%) patients achieved Engel class Ia outcomes, indicating seizure freedom, while none of the patients experienced clinically significant permanent postoperative neurological deficits. Resective surgery with intraoperative brain mapping under awake conditions was a valid treatment option for achieving a cure in cases of drug-resistant focal epilepsy, even in situations in which the condition is considered inoperable due to the risk of significant postoperative neurological deficits.

Adaptive control scheme for cooperative transport systems navigation under uncertainty

An adaptive robust control scheme for a cooperative transport system is proposed to tackle the challenges arising from parameter uncertainty, external interference, measurement errors, and other factors. The cooperative transport system consists of a leader automated ground vehicle, a baggage carrier, and a follower automated ground vehicle. Firstly, a mechanics-based independent dynamic model without constraints is established for each component within the system, and the coupling relationship between components is analyzed to design the constraint function. Secondly, to address inaccuracies in initial conditions, the trajectory errors in both their zero- and first-order forms are introduced. A closed-form dynamic model that is subject to constraints is then developed for the entire cooperative system, incorporating both structural and performance constraints. Thirdly, an innovative adaptive robust control scheme is introduced for mechanical systems facing uncertainty. An adaptive law is devised to estimate the bounds of uncertainty. The control is deterministic and can be mathematically expressed in a closed-form. Fourthly, a constrained optimization problem is formulated using the fuzzy information of uncertainty to choose an appropriate optimal gain kopt of the adaptive law. This is achieved by minimizing the combination of average fuzzy system performance and control effort. Finally, numerical simulations are conducted to verify the effectiveness and adaptability of the proposed control method. The performance of controlled cooperative transport system is both deterministically guaranteed and fuzzily optimized.

A semi-definite optimization method for maximizing the shared band gap of topological photonic crystals

Topological photonic crystals (PCs) can support robust edge modes to transport electromagnetic energy in an efficient manner. Such edge modes are the eigenmodes of the PDE operator for a joint optical structure formed by connecting together two photonic crystals with distinct topological invariants, and the corresponding eigenfrequencies are located in the shared band gap of two individual photonic crystals. This work is concerned with maximizing the shared band gap of two photonic crystals with different topological features in order to increase the bandwidth of the edge modes. We develop a semi-definite optimization framework for the underlying optimal design problem, which enables efficient update of dielectric functions at each time step while respecting symmetry constraints and, when necessary, the constraints on topological invariants. At each iteration, we perform sensitivity analysis of the band gap function and the topological invariant constraint function to linearize the optimization problem and solve a convex semi-definite programming (SDP) problem efficiently. Numerical examples show that the proposed algorithm is superior in generating optimized optical structures with robust edge modes.

Upper limb exoskeleton rehabilitation robot inverse kinematics modeling and solution method based on multi-objective optimization

The inverse kinematics problem of exoskeleton rehabilitation robots is challenging due to the lack of a standard analytical model, resulting in a complex and varied solution process. This complexity is especially pronounced in redundant upper limb exoskeleton robots, where inefficient solutions hinder the robot’s ability to adapt to the kinematic shape of the upper limb. This paper proposes a modeling and solution method based on multi-objective optimization to address the inverse kinematics of upper limb exoskeleton robots. We analyzed and validated this method using a redundant upper limb exoskeleton rehabilitation robot system developed by ourselves. First, we established a multi-objective inverse kinematics solution model by defining the end-position function, joint motion comfort function, system energy consumption function, motion safety, and human-like constraints. Then, the solution was designed based on the Improved Equilibrium Optimization (IEO) algorithm and validated its computational performance in terms of optimization ability, accuracy, and robustness. Finally, we experimentally tested the inverse kinematics solution model with the IEO algorithm on discrete objectives and continuous training trajectories using a redundant upper limb exoskeleton rehabilitation robot system. The results show that by incorporating the joint comfort function, system energy consumption function, and human-like constraints into the inverse kinematics model, we can not only quickly solve the inverse kinematics of redundant upper limb exoskeleton robots but also significantly improve the robot’s motion shape. Furthermore, it has better solution accuracy and stronger robustness than other algorithms when solving this inverse kinematics model based on the IEO algorithm.

Deciphering the influence of evolutionary legacy and functional constraints on the patella: an example in modern rhinoceroses amongst perissodactyls.

In mammals, the patella is the biggest sesamoid bone of the skeleton and is of crucial importance in posture and locomotion, ensuring the role of a pulley for leg extensors while protecting and stabilizing the knee joint. Despite its central biomechanical role, the relation between the shape of the patella and functional factors, such as body mass or locomotor habit, in the light of evolutionary legacy are poorly known. Here, we propose a morphofunctional investigation of the shape variation of the patella among modern rhinoceroses and more generally among perissodactyls, this order of ungulates displaying a broad range of body plan, body mass and locomotor habits, to understand how the shape of this sesamoid bone varies between species and relatively to these functional factors. Our investigation, relying on three dimensional geometric morphometrics and comparative analyses, reveals that, within Rhinocerotidae and between the three perissodactyl families, the shape of the patella strongly follows the phylogenetic affinities rather than variations in body mass. The patellar shape is more conservative than initially expected both within and between rhinoceroses, equids and tapirs. The development of a medial angle, engendering a strong mediolateral asymmetry of the patella, appears convergent in rhinoceroses and equids, while tapirs retain a symmetric bone close to the plesiomorphic condition of the order. This asymmetric patella is likely associated with the presence of a "knee locking" mechanism in both equids and rhinos. The emergence of this condition may be related to a shared locomotor habit (transverse gallop) in both groups. Our investigation underlines unexcepted evolutionary constraints on the shape of a sesamoid bone usually considered as mostly driven by functional factors.

Multi-scale self-attention feature decoupling transfer network-based cross-domain capacity prediction of lithium-ion batteries

Lithium-ion battery capacity prediction is paramount for improving the safety and reliability of energy storage devices. However, accurately predicting capacity continues to pose a challenge, stemming from the diverse range of operational conditions and the lack of capacity labels under unpredictable scenarios. To tackle this problem, a multi-scale self-attention feature decoupling transfer network is proposed for predicting the capacity of lithium-ion batteries across diverse operational conditions. More specifically, multi-scale multi-head self-attentive encoders are designed to adaptively extract multi-scale domain-invariant features by using a series of loss function constraints. Then, transfer learning integrated with domain-invariant features is applied to migrate the knowledge of the source domain to the target domain for cross-domain capacity prediction. Finally, the performance of our methods is authenticated through utilization of two battery dataset, each including three different charging and discharging scenarios. Experimental results indicate that the proposed method effectively extracts domain-invariant features from charging data characterized by varying distributions, thereby mitigating the effects of distributional differences. Compared with the state-of-the-art methods, the proposed method shows excellent accuracy and bustling ability in two datasets.

Enhanced Chaotic Pseudorandom Number Generation Using Multiple Bernoulli Maps with Field Programmable Gate Array Optimizations

Certain methods for implementing chaotic maps can lead to dynamic degradation of the generated number sequences. To solve such a problem, we develop a method for generating pseudorandom number sequences based on multiple one-dimensional chaotic maps. In particular, we introduce a Bernoulli chaotic map that utilizes function transformations and constraints on its control parameter, covering complementary regions of the phase space. This approach allows the generation of chaotic number sequences with a wide coverage of phase space, thereby increasing the uncertainty in the number sequence generation process. Moreover, by incorporating a scaling factor and a sine function, we develop a robust chaotic map, called the Sine-Multiple Modified Bernoulli Chaotic Map (SM-MBCM), which ensures a high degree of randomness, validated through statistical mechanics analysis tools. Using the SM-MBCM, we propose a chaotic PRNG (CPRNG) and evaluate its quality through correlation coefficient analysis, key sensitivity tests, statistical and entropy analysis, key space evaluation, linear complexity analysis, and performance tests. Furthermore, we present an FPGA-based implementation scheme that leverages equivalent MBCM variants to optimize the electronic implementation process. Finally, we compare the proposed system with existing designs in terms of throughput and key space.

Cytonuclear evolution in fully heterotrophic plants: lifestyles and gene function determine scenarios

BackgroundEvidence shows that full mycoheterotrophs and holoparasites often have reduced plastid genomes with rampant gene loss, elevated substitution rates, and deeply altered to conventional evolution in mitochondrial genomes, but mechanisms of cytonuclear evolution is unknown. Endoparasitic Sapria himalayana and mycoheterotrophic Gastrodia and Platanthera guangdongensis represent different heterotrophic types, providing a basis to illustrate cytonuclear evolution. Here, we focused on nuclear-encoded plastid / mitochondrial (N-pt / mt) -targeting protein complexes, including caseinolytic protease (ClpP), ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCo), oxidative phosphorylation system (OXPHOS), DNA recombination, replication, and repair (DNA-RRR) system, and pentatricopeptide repeat (PPR) proteins, to identify evolutionary drivers for cytonuclear interaction.ResultsThe severity of gene loss of N-pt PPR and pt-RRR genes was positively associated with increased degree of heterotrophy in full mycoheterotrophs and S. himalayana, while N-mt PPR and mt-RRR genes were retained. Substitution rates of organellar and nuclear genes encoding N-pt/mt subunits in protein complexes were evaluated, cytonuclear coevolution was identified in S. himalayana, whereas disproportionate rates of evolution were observed in the OXPHOS complex in full mycoheterotrophs, only slight accelerations in substitution rates were identified in N-mt genes of full mycoheterotrophs.ConclusionsNuclear compensatory evolution was identified in protein complexes encoded by plastid and N-pt genes. Selection shaping codon preferences, functional constraint, mt-RRR gene regulation, and post-transcriptional regulation of PPR genes all facilitate mito-nuclear evolution. Our study enriches our understanding of genomic coevolution scenarios in fully heterotrophic plants.

Approach for multi-valued integer programming in multi-material topology optimization: Random discrete steepest descent (RDSD) algorithm

The present study models the multi-material topology optimization problems as the multi-valued integer programming (MVIP) or named as combinatorial optimization. By extending classical convex analysis and convex programming to discrete point-set functions, the discrete convex analysis and discrete steepest descent (DSD) algorithm are introduced. To overcome combinatorial complexity of the DSD algorithm, we employ the sequential approximate integer programming (SAIP) to explicitly and linearly approximate the implicit objective and constraint functions. Considering the multiple potential changed directions for multi-valued design variables, the random discrete steepest descent (RDSD) algorithm is proposed, where a random strategy is implemented to select a definitive direction of change. To analytically calculate multi-material discrete variable sensitivities, topological derivatives with material contrast is applied. In all, the MVIP is finally transferred as the linear 0–1 programming that can be efficiently solved by the canonical relaxation algorithm (CRA). Explicit nonlinear examples demonstrate that the RDSD algorithm owns nearly three orders of magnitude improvement compared with the commercial software (GUROBI). The proposed approach, without using any continuous variable relaxation and interpolation penalization schemes, successfully solves the minimum compliance problem, strength-related problem, and frequency-related optimization problems. Given the algorithm efficiency, mathematical generality and merits over other algorithms, the proposed RDSD algorithm is meaningful for other structural and topology optimization problems involving multi-valued discrete design variables.

Multi-objective optimization of FCC separation system based on NSGA-Ⅱ

Based on the industrial production data, the simulation of the separation process of a 2 million tons/year FCC unit including the fractionation and the absorption-stabilization systems were conducted on Aspen Plus software. To optimize the operation process, multi-objective optimization was performed integrating the Aspen Plus platform and MATLAB environment utilizing the improved non-dominated sorting genetic algorithm (NSGA-Ⅱ). The established multi-objective optimization model was used for the operating variable screening, the genetic algebra selection and the optimal solution determination. During the optimization, the total yield of LPG and stable gasoline was aimed as the first optimization objective while the energy consumption of the whole system as the second objective. Five expressions were applied as the constraint functions and nine operating variables were conducted as the decision variables. The results showed that the performances of FCC separation system have been greatly improved after optimization. Some optimization strategies are advised for the whole system. The total yield of LPG and stabilized gasoline increases by 2. 44 %, and the energy consumption of the separation system decreases by 41. 79 %. In addition, the CO2 emission is reduced by 23.59 t/h and the total annual cost (TAC) is reduced by $0.89 million/year. It has been revealed that the multi-objective optimization method based on NSGA-Ⅱ algorithm is useful for the guidance of the optimization of industrial petrochemical process.

Long range segmentation of prokaryotic genomes by gene age and functionality.

Bacterial and archaeal genomes encompass numerous operons that typically consist of two to five genes. On larger scales, however, gene order is poorly conserved through the evolution of prokaryotes. Nevertheless, non-random localization of different classes of genes on prokaryotic chromosomes could reflect important functional and evolutionary constraints. We explored the patterns of genomic localization of evolutionarily conserved (ancient) and variable (young) genes across the diversity of bacteria and archaea. Nearly all bacterial and archaeal chromosomes were found to encompass large segments of 100-300 kb that were significantly enriched in either ancient or young genes. Similar clustering of genes with lethal knockout phenotype (essential genes) was observed as well. Mathematical modeling of genome evolution suggests that this long-range gene clustering in prokaryotic chromosomes reflects perpetual genome rearrangement driven by a combination of selective and neutral processes rather than evolutionary conservation.